The spectral picture and the closure of the similarity orbit of strongly irreducible operators |
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Authors: | Chun-Ian Jiang Zong-yao Wang |
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Institution: | (1) Department of Mathematics, Jilin University, 130023 Changchun, P. R. China;(2) Department of Mathematics, East China University of Science and Technology, 200237 Shanghai, P. R. China |
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Abstract: | An operator on a complex, separable, infinite dimensional Hilbert space is strongly irreducible if it does not commute with any nontrivial idempotent. This article answers the following questions of D. A. Herrero: (i) Given an operatorT with connected spectrum, can we find a strongly irreducible operatorL such that they have same spectral picture? (ii) When we use a sequence of irreducible operators to approximateT, can the approximation be the “most economic”? i.e., does there exist a strongly irreducible operatorL such thatT ∈S(L) ? (the closure of the similarity orbit ofL)? It is shown that the answer for the two questions is yes. |
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Keywords: | Primary 47A15 Secondary 47A10 |
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